Abstract
We show that the Hilbert scheme of two points on the Vinberg surface has a two-to-one map onto a very symmetric EPW sextic in . The fourfold is singular along planes, of which form a complete family of incident planes. This solves a problem of Morin and O’Grady and establishes that is the maximal cardinality of such a family of planes. Next, we show that this Hilbert scheme is birationally isomorphic to the Kummer-type IHS fourfold constructed by Donten-Bury and Wiśniewski [On 81 symplectic resolutions of a 4–dimensional quotient by a group of order , preprint (2014)]. We find that is also related to the Debarre–Varley abelian fourfold.
Citation
Maria Donten-Bury. Bert van Geemen. Grzegorz Kapustka. Michał Kapustka. Jarosław Wiśniewski. "A very special EPW sextic and two IHS fourfolds." Geom. Topol. 21 (2) 1179 - 1230, 2017. https://doi.org/10.2140/gt.2017.21.1179
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